There is a continuing need for higher performance digital data communications systems. Perhaps nowhere is this need more evident than on the worldwide packet data communications network now commonly referred to as the “Internet.” On the Internet, the “richness” of content is constantly increasing, requiring an ever-increasing amount of bandwidth to provide Internet content to users. As a result of this increased demand for bandwidth, significant efforts have been made to develop new types of high-speed digital data communications systems. For example, optical fiber based networks are being built in many large metropolitan areas and undersea to connect continents. As another example, new wireless protocols are being developed to provide Internet content to many different types of small, portable devices.
One of the significant drawbacks of deploying many of these new types of high-speed digital data communications systems is the high cost and amount of time required to develop and build out the new infrastructure required by the systems. Because of these high costs, many new high-speed digital data communications systems are initially deployed only in densely populated areas, where the cost of building out the new infrastructure can be quickly recovered. Less populated areas must often wait to receive the new communications systems and some rural areas never receive the new systems where it is not cost effective to build the infrastructure.
For several reasons, significant efforts are being made to utilize conventional twisted pair telephone lines to provide high-speed digital data transmission. First, a significant amount of twisted pair telephone line infrastructure already exists in many countries. Thus, using conventional twisted pair telephone lines avoids the cost of building expensive new infrastructure. Second, conventional twisted pair telephone lines extend into customers' homes and businesses, avoiding the so-called “last mile” problem. As a result of recent development efforts in this area, several new communications protocols, such as ADSL, G.Lite and VDSL, have been developed for providing high-speed digital transmission over conventional twisted pair telephone lines.
Despite the advantages to using conventional twisted pair telephone lines to provide high-speed digital communications, there are some problems with this approach. First, conventional twisted pair telephone lines cause signal attenuation per unit length that increases rapidly with frequency. A moderate length twisted pair line, for example around fifteen thousand feet, may cause only a few decibels (dB) of attenuation in the voice band, for which the line was originally designed, but many tens of dB of attenuation at higher transmission frequencies, for example around 1.1 MHz for ADSL. This results in a transfer function with a wide dynamic range, making channel equalization more difficult. The transfer function is further complicated by bridge taps and impedance mismatches between line sections that cause reflections and echoes at the receiver. Furthermore, filtering performed at the transmitter and receiver also increases the complexity of the transfer function.
The standards for ADSL and G.Lite specify Discrete Multitone (DMT) modulation. DMT is also under consideration for use in VDSL systems. DMT modulation generally involves transmitting digital data on a number of carriers simultaneously. Modulation and demodulation are performed using a Fast Fourier Transform (FFT). A cyclic prefix is introduced to ensure separation between successive DMT symbols and eliminate inter-symbol interference (ISI). In practice, the cyclic prefix is necessarily quite short, generally much shorter than the impulse response of the communications channel. This often results in significant ISI being present in the received data. Large amounts of ISI cause a large reduction in the available communications bandwidth. This is especially true for long twisted pair telephone lines likely to be encountered in ADSL and VDSL communications systems. The effect of this ISI is to reduce the SNR in each bin of the FFT demodulator employed in a DMT system.
Standard equalizers used in digital communication systems, such as adaptive LMS and RLS equalizers, are generally inappropriate for DMT systems since they are not designed to eliminate ISI. The current state of the art in equalizer design has the objective of shortening the overall channel plus equalizer impulse response so that the overall response is shorter than the cyclic prefix length. Various attempts to meet this requirement have been made. See for example, Optimal Filtering, by B. D. O. Anderson and J. B. Moore, Prentice-Hall, 1979; and A Multicarrier Primer, by J. M. Cioffi. Determining equalizer coefficients is generally a computationally inefficient process and can be quite sensitive to noise, which limits the practical application of these techniques.
In addition to the equalization problem, twisted pair lines suffer from various forms of interference. Up to fifty twisted pairs are conventionally grouped together in binders. As a result, a signal on one pair can cause interference on other pairs in the same binder. This interference is called crosstalk and results in a reduced signal-to-noise ratio (SNR) at the receiver. Current approaches to mitigate crosstalk require access to the signal transmitted on the interfering line. This makes current approaches useful only in a central office environment, where the signals on all pairs in a binder are available. Thus, none of the existing crosstalk mitigation approaches are suitable when only the received signal is available.
Another problem is that conventional approaches for processing data received from a communications channel consider only the noise on the communications channel, leading to sub-optimal results. There is generally no consideration given to the frequency domain response of the equalizer and hence, there is no guarantee against SNR loss due to roundoff error in finite precision arithmetic. In addition to roundoff error in the equalizer, there is also roundoff error in the fast Fourier transform (FFT) used in DMT receivers. Prior channel equalization approaches do not take this source of noise into account. Where 16-bit fixed-point arithmetic is used in the FFT, the roundoff error in the FFT can be quite significant, and must be taken into account if overall SNR is to be maintained.
Based on the foregoing, there is a need for an approach for processing data received from a communications channel in finite precision arithmetic applications that does not suffer from the limitations of conventional approaches.